On the extent of star countable spaces

O.T. Alas, L.R. Junqueira, J. van Mill, V.V. Tkachuk, R.G. Wilson

Research output: Contribution to JournalArticleAcademicpeer-review


For a topological property P, we say that a space X is star P if for every open cover U of the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω
Original languageEnglish
Pages (from-to)603-615
JournalCentral European Journal of Mathematics
Publication statusPublished - 2011


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